Theorem simp3i 1141

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1138	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1087

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1089

This theorem is referenced by:  hartogslem2  9537  harwdom  9585  divalglem6  16340  structfn  17088  strleun  17089  oppchomfval  17657  sratset  20802  srads  20805  tngip  24161  dfrelog  26073  log2ub  26451  birthdaylem3  26455  birthday  26456  divsqrtsum2  26484  harmonicbnd2  26506  lgslem4  26800  lgscllem  26804  lgsdir2lem2  26826  lgsdir2lem3  26827  mulog2sumlem1  27034  siilem2  30100  h2hva  30222  h2hsm  30223  h2hnm  30224  elunop2  31261  wallispilem3  44773  wallispilem4  44774  prstchomval  47684